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If x and y are positive integers, is x even?
(1) xy + yx is even.
(2) yx + 4x is odd.
(2) yx + 4x is odd.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx...
Statement (1): xy + yx is even.
The sum of xy + yx can be simplified to 2xy, which is even. This statement implies that 2xy is even, but it doesn't provide any information about the value of x or y individually. Therefore, statement (1) alone is not sufficient to determine if x is even.
The sum of xy + yx can be simplified to 2xy, which is even. This statement implies that 2xy is even, but it doesn't provide any information about the value of x or y individually. Therefore, statement (1) alone is not sufficient to determine if x is even.
Statement (2): yx + 4x is odd.
If yx + 4x is odd, it means that the sum of yx and 4x is odd. This implies that both terms must have the same parity (either both even or both odd) since the sum of two terms with different parity would be even. Since 4x is always even (for any positive integer x), it means that yx must also be even. However, we still don't know the specific values of x and y, so we cannot determine if x is even or odd. Statement (2) alone is not sufficient to determine if x is even.
If yx + 4x is odd, it means that the sum of yx and 4x is odd. This implies that both terms must have the same parity (either both even or both odd) since the sum of two terms with different parity would be even. Since 4x is always even (for any positive integer x), it means that yx must also be even. However, we still don't know the specific values of x and y, so we cannot determine if x is even or odd. Statement (2) alone is not sufficient to determine if x is even.
Combining both statements, we know that 2xy is even (from statement 1) and yx is even (implied by statement 2). This means that both xy and yx must be even. If both xy and yx are even, it implies that x and y are both even. Therefore, by considering both statements together, we can conclude that x is even. Hence, both statements together are sufficient to answer the question.
The answer is option C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
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If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx...
Statement (1): xy = yx is even.
This statement tells us that the product of x and y is even. We know that if a number is even, it can be represented as 2n, where n is an integer. Therefore, we can write xy = 2n.
Statement (2): yx + 4x is odd.
This statement tells us that the sum of yx and 4x is odd. We know that if a number is odd, it cannot be represented as 2n, where n is an integer. Therefore, we can write yx + 4x = 2m + 1.
Combined analysis:
To determine if x is even, we need to consider both statements together.
If we combine the equations from both statements, we get:
xy = 2n and yx + 4x = 2m + 1.
Now, let's consider the possible values of x and y:
- If x = 1 and y = 2, then xy = yx = 2, which is even. But yx + 4x = 2 + 4 = 6, which is even. Therefore, x is not necessarily even.
- If x = 2 and y = 1, then xy = yx = 2, which is even. But yx + 4x = 2 + 8 = 10, which is even. Therefore, x is not necessarily even.
- If x = 2 and y = 2, then xy = yx = 4, which is even. But yx + 4x = 4 + 8 = 12, which is even. Therefore, x is not necessarily even.
From these examples, we can see that x can be even or odd depending on the values of x and y. Therefore, both statements together are not sufficient to determine if x is even.
Hence, the correct answer is option E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
This statement tells us that the product of x and y is even. We know that if a number is even, it can be represented as 2n, where n is an integer. Therefore, we can write xy = 2n.
Statement (2): yx + 4x is odd.
This statement tells us that the sum of yx and 4x is odd. We know that if a number is odd, it cannot be represented as 2n, where n is an integer. Therefore, we can write yx + 4x = 2m + 1.
Combined analysis:
To determine if x is even, we need to consider both statements together.
If we combine the equations from both statements, we get:
xy = 2n and yx + 4x = 2m + 1.
Now, let's consider the possible values of x and y:
- If x = 1 and y = 2, then xy = yx = 2, which is even. But yx + 4x = 2 + 4 = 6, which is even. Therefore, x is not necessarily even.
- If x = 2 and y = 1, then xy = yx = 2, which is even. But yx + 4x = 2 + 8 = 10, which is even. Therefore, x is not necessarily even.
- If x = 2 and y = 2, then xy = yx = 4, which is even. But yx + 4x = 4 + 8 = 12, which is even. Therefore, x is not necessarily even.
From these examples, we can see that x can be even or odd depending on the values of x and y. Therefore, both statements together are not sufficient to determine if x is even.
Hence, the correct answer is option E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?.
If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If x and y are positive integers, is x even?(1) xy + yx is even.(2) yx + 4x is odd.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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